Yet another optimization problem... if anyone knows how to solve this please explain it to me:

Thank you.A box with a square base and open top must have a volume of 32,000cm3. Find the dimensions of the box that minimize the amount of material used.

Set up an equation for the amount of material used as a function of one of the dimensions of the box. If H is the height and L the dimension of the square base, then you know that:

32000 = HL^2

The area of material used is the sum of the areas of the four sides plus the top & bottom: A = 4HL + 2*L^2.

You can combine these to get an equation that gives A as a function of L. Then use the technique I described in response to the other question you posted to solve for the value for L that gives a minimum value for A.

You must minimize the surface area given the volume is x^{2}y=32,000

Since there is no top, the surface area is given by S=x^{2}+4xy

Solve the volume equation for, say, y; Sub it into S; differentiate, set to 0 and solve for x.

The y value will then follow.